CUET Mathematics 2023 22 May Shift 3 PYQs

4

0

11

5

$f(x) + g(x)$

$f(x) - g(x)$

$f(x) \cdot g(x)$

$\frac{g(x)}{f(x)}$

$a = 2, b = 3$

$a = 3, b = 2$

$a = -2, b = 3$

$a = 2, b = -3$

$(-\infty, -1]$

$(-\infty, -1] \cup [2, \infty)$

$[-1, 2]$

$[2, \infty)$

(A) and (B) Only

(B) and (C) Only

(D) and (E) Only

(B), (D) and (E) Only

(0, 6)

(5, 4)

(4, 8)

(4, 0)

$^5C_4 \left(\frac{4}{5}\right)^4 \frac{1}{5}$

$\left(\frac{4}{5}\right)^4 \frac{1}{5}$

$^5C_4 \left(\frac{1}{5}\right)^4 \left(\frac{4}{5}\right)$

$\left(\frac{1}{5}\right)^4 \left(\frac{4}{5}\right)$

3

5

7

10

-24

-4

4

-6

$\frac{d^2y}{dx^2} + b^2 y = 0$

$\frac{dy}{dx} + b^2 y = 0$

$\frac{d^2y}{dx^2} - b^2 y = 0$

$\frac{d^2y}{dx^2} + y = 0$

$(A')' = A$

$(KA)' = KA'$ (Where K is any constant)

$(A + B)' = B' + A'$

$(AB)' = A'B'$

$\frac{\pi}{2}$

$\frac{\pi}{4}$

$\tan^{-1} \frac{4}{3}$

$\tan^{-1} \frac{4\sqrt{2}}{7}$

$\tan^{-1} \frac{32}{27}$

$\tan^{-1} \frac{27}{32}$

$\log \frac{32}{27}$

$\log \frac{27}{32}$

$3 \int_0^4 \sqrt{9 - x^2} \, dx$

$\frac{3}{4} \int_0^4 \sqrt{9 - x^2} \, dx$

$3 \int_0^4 \sqrt{16 - x^2} \, dx$

$\frac{3}{4} \int_0^4 \sqrt{16 - x^2} \, dx$

$\frac{e^x}{1+x^2} + C$

$-\frac{e^x}{1+x^2} + C$

$\frac{e^x}{(1+x^2)^2} + C$

$-\frac{e^x}{(1+x^2)^2} + C$

$-\frac{1}{3}\hat{i} + \frac{4}{3}\hat{j} + \frac{1}{3}\hat{k}$

$-3\hat{i} + 3\hat{k}$

$3\hat{i} - 3\hat{k}$

$\frac{1}{3}\hat{i} - \frac{4}{3}\hat{j} - \frac{1}{3}\hat{k}$

$2\sqrt{2}$

$2(\sqrt{2} + 1)$

$2$

$2(\sqrt{2} - 1)$

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{1}{18}$

$\frac{1}{9}$

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A)-(IV), (B)-(I), (C)-(III), (D)-(II)

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(II), (B)-(IV), (C)-(III), (D)-(I)

(A) and (B) Only

(A) and (D) Only

(B) and (C) Only

(C) and (D) Only

1

2

3

$\frac{3}{2}$

$\frac{3}{5}$

$\frac{4}{11}$

$\frac{23}{55}$

$\frac{2}{5}$

$\frac{8}{3}$ sq. units

$\frac{8}{5}$ sq. units

3 sq. units

8 sq. units

$x$

$e^x$

$\log_e x$

$\log_e (\log_e x)$

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{3\pi}{4}$

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

(A)-(I), (B)-(III), (C)-(IV), (D)-(II)

$e^x \log_e \sec x + C$

$\log_e \sec x + C$

$e^x \tan x + C$

$e^x \sec x + C$

$\frac{ab \cos x}{a^2 - b^2 \sin^2 x}$

$\frac{ab \cos x}{a^2 + b^2 \sin^2 x}$

$\frac{a \sin x}{a^2 - b^2 \sin^2 x}$

$\frac{2ab \cos x}{a^2 - b^2 \sin^2 x}$

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

unbounded in first quadrant

unbounded in first and second quadrant

bounded in first quadrant

not feasible

$x \sec t + y \csc t = a$

$x \sec t - y \csc t = a$

$x \csc t + y \sec t = a$

$x \csc t - y \sec t = a$

(A) and (B) Only

(A), (B) and (D) Only

(A), (C) and (D) Only

(B) and (D) Only

$\left\{\frac{5}{4}\right\}$

$\left\{-\frac{5}{4}, \frac{5}{4}\right\}$

$\left\{\frac{11}{4}\right\}$

$\mathbf{R} - \left\{\frac{11}{4}\right\}$

$\frac{1}{2\pi}$ unit

$\frac{1}{\pi}$ unit

$\frac{\pi}{2}$ unit

$\pi$ unit

(A)-(I), (B)-(II), (C)-(IV), (D)-(III)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

(A)-(IV), (B)-(II), (C)-(III), (D)-(I)

(A) and (C) Only

(A) and (B) Only

(A) and (D) Only

(B) and (C) Only

$12\pi$ sq. units

$8\pi$ sq. units

$4\pi$ sq. units

$2\pi$ sq. units

$x + y = 250$

$x + y \leq 250$

$x + y \geq 250$

$x + y > 250$

$2!$

$3!$

$4!$

$5!$

$3x - y + 2z = 0$

$3x - y + 2z = 20$

$2x - 4y + 5z = 0$

$2x - 4y + 5z = 45$

$-\frac{2\pi}{3}$

$\frac{2\pi}{3}$

$\frac{\pi}{3}$

$-\frac{\pi}{3}$

$0.06x^3$ m$^3$

$0.02x^3$ m$^3$

$3x^2$ m$^3$

$0.02x$ m$^3$

$\begin{pmatrix} \cos 4\theta & \sin 4\theta \\ -\sin 4\theta & \cos 4\theta \end{pmatrix}$

$\begin{pmatrix} \cos^2 2\theta & \sin^2 2\theta \\ \sin^2 2\theta & \cos^2 2\theta \end{pmatrix}$

$\begin{pmatrix} 1 & 0 \\ \sin 2\theta & \cos 2\theta \end{pmatrix}$

$\begin{pmatrix} \cos 6\theta & \sin 6\theta \\ -\sin 6\theta & \cos 6\theta \end{pmatrix}$

(A), (B), (D) Only

(A), (C) Only

(A), (B), (C) Only

(A), (D) Only

$\left[\frac{3}{2}, \infty\right)$

$\left[\frac{1}{2}, \infty\right)$

$\left(\frac{3}{2}, \infty\right)$

$\left[\frac{5}{2}, \infty\right)$

every integer

every even number

every real number

at zero only

87

89

90

85

$y = x^2 + \frac{5}{2}$

$y = \frac{x^2}{2} + 2$

$y = \frac{x^2}{3} + \frac{2}{3}$

$y = 3x^2 + 5$

0, -8

0, 8

2, 6

-2, 6

$-\sqrt[3]{\frac{y}{x}}$

$-3\sqrt{\frac{y}{x}}$

$\sqrt[3]{\frac{y}{x}}$

$-\sqrt{\frac{y}{x}}$

(4, 3)

(9, 0)

(2, 5)

(0, 8)

1

4

0

3

(C) Only

(A), (C) Only

(A), (E) Only

(B), (D) Only

(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

65 kg

75 kg

50 kg

100 kg

(A), (B), (D) Only

(A), (C), (D) Only

(B), (C) Only

(B), (C), (D) Only

(A), (B) Only

(A), (B), (C) Only

(B), (C), (D) Only

(C), (D) Only

Rs. 50,000

Rs. 4500

Rs. 3000

Rs. 40,000

$15\frac{1}{7}$ hours

$13\frac{1}{7}$ hours

$17\frac{1}{7}$ hours

$19\frac{1}{7}$ hours

432

476

676

576

Rs. 35897.29

Rs. 53897.29

Rs. 53798.29

Rs. 58973.29

125.50

120.50

124.50

126.50

2

10

Finite

Infinite

$\frac{14}{3}$

$\frac{14}{9}$

$\frac{14}{11}$

$\frac{70}{3}$

20 litres

25 litres

30 litres

40 litres

0

2

4

8

Rs. 22

Rs. 24

Rs. 20

Rs. 28

Margin of error

Alternate

Level of significance

Confidence interval

$\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 0$

$\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 0$

$\frac{d^2y}{dx^2} - 5\frac{dy}{dx} - 6y = 0$

$\frac{d^2y}{dx^2} + 5\frac{dy}{dx} - 6y = 0$

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(IV), (B)-(II), (C)-(I), (D)-(III)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(II), (B)-(III), (C)-(I), (D)-(IV)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

6.16%

8.16%

7.16%

8.26%

$\frac{1}{2}$

$\frac{1}{3}$

2

3

{2, 13, 24, 35, ----}

{16, 27, 38, 49, ----}

{5, 16, 27, 38, 49, ----}

{4, 15, 26, 37, ----}

9 : 12 : 14

6 : 12 : 11

9 : 14 : 12

12 : 9 : 14

$14b - 12a \geq 3$

$14a - 12b \geq 3$

$12a - 14b \geq 3$

$12b + 14a \leq -3$

Rs. 1433.33

Rs. 1233.33

Rs. 1033.33